75811 Specification

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© MEI/OCR 2013

Oxford Cambridge and RSA Examinations

MEI STRUCTURED MATHEMATICS

A Credit Accumulat ion Scheme for Advanced Mathematics

OCR ADVANCED SUBSIDIARY GCE IN MATHEMATICS (MEI) (3895)OCR ADVANCED SUBSIDIARY GCE IN FURTHER MATHEMATICS (MEI) (3896/3897)OCR ADVANCED SUBSIDIARY GCE IN PURE MATHEMATICS (MEI) (3898)

OCR ADVANCED GCE IN MATHEMATICS (MEI) (7895)OCR ADVANCED GCE IN FURTHER MATHEMATICS (MEI) (7896/7897)OCR ADVANCED GCE IN PURE MATHEMATICS (MEI) (7898)

QAN (3895) 100/3417/1 QAN (3896/3897) 100/6016/9 QAN (3898) 100/6017/0 QAN (7895) 100/3418/3 QAN (7896/7897) 100/6018/2

QAN (7898) 100/6019/4

Key Features

• Unrivalled levels of support and advice.

• Web-based resources covering the units.

• Clear and appropriate progression routes from GCSE for all students.

• Flexibility in provision of Further Mathematics.

• User friendly and accessible.

This specification was devised by Mathematics in Education and Industry (MEI) and is administered

by OCR.


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© MEI/OCR 2013

Support and Advice

The specification is accompanied by a complete support package provided by MEI and OCR. The twoorganisations work closely together with MEI taking responsibility for the curriculum and teaching aspects

of the course, and OCR the assessment.

• Advice is always available at the end of the telephone or by e-mail.

• One-day INSET courses provided by both MEI and OCR.

• The MEI annual three-day conference.

• MEI branch meetings.

• Regular newsletters from MEI.

• Specimen and past examination papers, mark schemes and examiners’ reports.

• Coursework resource materials and exemplar marked tasks.

Web-based Support

The units in this specification are supported by a very large purpose-built website designed to help students

and teachers.

Routes of Progression

This specification is designed to provide routes of progression through mathematics between GCSE andHigher Education and/or employment. It has the flexibility to meet the diverse needs of the wide variety of

students needing mathematics at this level.

Further Mathematics

A feature of this specification is the flexibility that it allows teachers in delivering Further Mathematics. It is

possible to teach this concurrently with AS and Advanced GCE Mathematics, starting both at the same time,or to teach the two courses sequentially, or some combination of the two.

User friendliness

This specification has been designed by teachers for students. Thus the accompanying text books, one for

each unit, are accessible to students, easy to read and work from. The Students’ Handbook provides a

particularly helpful source of information.

AS assessment June 2014A2 assessment June 2014

AS certification June 2014 GCE certification June 2014


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© MEI/OCR 2013 Contents 3 Oxford, Cambridge and RSA Examinations MEI Structured Mathematics

CONTENTS

Section A: SPECIFICATION SUMMARY 5

Section B: USER SUMMARY 7

Using this specification 7

Summary of Changes from the Previous MEI Specification 8

Section C: General Information 9

1 Introduction 9

1.1 Rationale 9

1.2 Certification title 12

1.3 Language 13

1.4 Exclusions 13

1.5 Key Skills 14

1.6 Code of Practice Requirements 14

1.7 Spiritual, Moral, Ethical, Social and Cultural Issues 14

1.8 Environmental Education, European Dimension and Health and Safety Issues 15

1.9 Avoidance of Bias 15

1.10 Calculators and computers 15

2 Specif ication Aims 16

2.1 Aims of MEI 16

2.2 Aims of this specification 16

3 Assessment Object ives 17

3.1 Application to AS and A2 17 3.2 Specification Grid 18

4 Scheme of Assessment 19

4.1 Units of Assessment 19

4.2 structure 20

4.3 Rules of Combination 22

4.4 Final Certification 25

4.5 Availability 27

4.6 Re-sits 27

4.7 Question Papers 28 4.8 Coursework 29

4.9 Special Arrangements 31

4.10 Differentiation 32

4.11 Grade Descriptions 32

5 Subject Content 34

5.1 Assumed Knowledge 34

5.2 Modelling 35

5.3 Competence Statements 36


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4 Contents © MEI/OCR 2013MEI Structured Mathematics Oxford, Cambridge and RSA Examinations

6 Unit Specifications 37

6.1 Introduction to Advanced Mathematics, C1 (4751) AS 37

6.2 Concepts for Advanced Mathematics, C2 (4752) AS 47

6.3 Methods for Advanced Mathematics, C3 (4753) A2 55

6.4 Applications of Advanced Mathematics, C4 (4754) A2 67

6.5 Further Concepts for Advanced Mathematics, FP1 (4755) AS 73

6.6 Further Methods for Advanced Mathematics, FP2 (4756) A2 81

6.7 Further Applications of Advanced Mathematics, FP3 (4757) A2 93

6.8 Differential Equations, DE (4758) A2 105

6.9 Mechanics 1, M1 (4761) AS 115

6.10 Mechanics 2, M2 (4762) A2 123

6.11 Mechanics 3, M3 (4763) A2 129

6.12 Mechanics 4, M4 (4764) A2 137

6.13 Statistics 1, S1 (4766) AS 143

6.14 Statistics 2, S2 (4767) A2 153 6.15 Statistics 3, S3 (4768) A2 159

6.16 Statistics 4, S4 (4769) A2 165

6.17 Decision Mathematics 1, D1 (4771) AS 175

6.18 Decision Mathematics 2, D2 (4772) A2 181

6.19 Decision Mathematics Computation, DC (4773) A2 187

6.20 Numerical Methods, NM (4776) AS 193

6.21 Numerical Computation, NC (4777) A2 201

6.22 Further Pure Mathematics with Technology, FPT (4798) A2 207

7 Further Information and Training for Teachers 214 Appendix A: Mathematical Formulae 215

Appendix B: Mathematical Notat ion 217

Vertical black lines indicate a significant change to the previous printed version.


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© MEI/OCR 2013 Section A: Specification Summary 5 Oxford, Cambridge and RSA Examinations MEI Structured Mathematics

SECTION A: SPECIFICATION SUMMARY

The units in MEI Structured Mathematics form a step-by-step route of progression through thesubject, from GCSE into the first year of university. For those who are insecure about their

foundation, access to the scheme is provided by the Free Standing Mathematics Qualification,

Foundations of Advanced Mathematics.

The subject is developed consistently and logically through the 22 AS and A2 units, following

strands of Pure Mathematics, Mechanics, Statistics, Decision Mathematics and Numerical Analysis.

Each unit is designed both as a worthwhile and coherent course of study in its own right, taking about45 hours of teaching time, and as a stepping stone to further work.

Suitable combinations of three and six modules give rise to AS and Advanced GCE qualifications inMathematics, Further Mathematics and Pure Mathematics. Candidates usually take their units at

different stages through their course, accumulating credit as they do so.

The normal method of assessment is by unit examinations, held in June each year, in most cases

lasting 1½ hours. Three units also have coursework requirements. Candidates are allowed to re-situnits, with the best mark counting.


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6 Section A: Specification Summary © MEI/OCR 2013 MEI Structured Mathematics Oxford, Cambridge and RSA Examinations

The Advanced Subsidiary GCE is assessed at a standard appropriate for candidates who havecompleted the first year of study of a two-year Advanced GCE course, i.e. between GCSE and

Advanced GCE. It forms the first half of the Advanced GCE course in terms of teaching time and

content. When combined with the second half of the Advanced GCE course, known as ‘A2’, theadvanced Subsidiary forms 50% of the assessment of the total Advanced GCE. However the

Advanced Subsidiary can be taken as a stand-alone qualification. A2 is weighted at 50% of the total

assessment of the Advanced GCE.


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© MEI/OCR 2013 Section B: User Summary 7 Oxford, Cambridge and RSA Examinations MEI Structured Mathematics

SECTION B: USER SUMMARY

USING THIS SPECIFICATION

This specification provides a route of progression through mathematics between GCSE and HigherEducation and/or employment.

• Students start with AS Mathematics. This consists of the two AS units in Pure Mathematics, C1 and C2, together with one applied unit, either M1, S1 or D1.

• Many students take one year over AS Mathematics but this is not a requirement; they can take alonger or a shorter time, as appropriate to their circumstances.

• Examinations are available in June only.

• Unit results are notified in the form of a grade and a Uniform Mark. The total of a candidate’sUniform Marks on relevant modules determines the grade awarded at AS GCE (or Advanced

GCE).

• A unit may be re-sat any number of times with the best result standing.

• To obtain an AS award a ‘certification entry’ must be made to OCR. There is no requirementfor candidates going on to Advanced GCE to make such an entry.

• To complete Advanced GCE Mathematics, candidates take three more units, C3, C4 and anotherapplied unit.

• The applied unit may be in the same strand as that taken for AS in which case it will be an A2unit (e.g. S2 following on from S1). Alternatively it may be in a different strand in which case itwill be an AS unit (e.g. M1 following on from S1).

• Many candidates will take these three units in the second year of their course but there is norequirement for this to be the case.

• An Advanced GCE award will only be made to those who apply for it.

• Candidates may also take Further Mathematics at AS and Advanced GCE. There isconsiderable flexibility in the way that this can be done.

• AS Further Mathematics consists of FP1 and two other units which may be AS or A2.

• The three units for AS Further Mathematics may be taken in the first year. The compulsory unitFP1 has been designed to be accessible for students who have completed Higher Tier GCSE

and are studying C1 and C2 concurrently. The AS units, M1, S1, D1 and NM are also suitable

for those taking AS Further Mathematics in the first year.

• Many of those who take AS Further Mathematics in the first year then take another three unitsin their second year to obtain Advanced GCE Further Mathematics. Such candidates take 12

units, six for Mathematics and six for Further Mathematics.

• Other AS Further Mathematics students spread their study over two years rather thancompleting it in the first year.

• Another pattern of entry is for candidates to complete Advanced GCE Mathematics in their firstyear and then to go onto Further Mathematics in their second year.

• Those who take Advanced GCE Mathematics and AS Further Mathematics must do at least9 units.

• Those who take Advanced GCE Mathematics and Advanced GCE Further Mathematics must doat least 12 units. The Further Mathematics must include both FP1 and FP2.


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8 Section B: User Summary © MEI/OCR 2013 MEI Structured Mathematics Oxford, Cambridge and RSA Examinations

• The rules of aggregation mean that it is to candidates’ advantage to certificate Advanced GCEMathematics and AS or Advanced GCE Further Mathematics at the same time. This can be

achieved, if necessary, by recertificating for any previously entered qualification in any series

when an entry for a qualification is made.

• Candidates who take 15 or 18 units are eligible for additional awards in Further Mathematics.

SUMMARY OF CHANGES FROM THE PREVIOUS MEI SPECIFICATION

The revisions to the subject criteria have resulted in considerable changes to the assessment

arrangements compared to those in the previous specification (those for first teaching in September

2000). These in turn have affected the provision of units in MEI Structured Mathematics and their

content:

• the core material is now covered in four units, two at AS and two at A2. The two AS units arecompulsory for Advanced Subsidiary Mathematics and all four core units are compulsory for

Advanced GCE Mathematics;

• consequently the first four units in the Pure Mathematics strand, C1 to C4 are all new;• only two applied units now contribute to Advanced GCE Mathematics;

• the reduction in the amount of Applied Mathematics in Advanced GCE Mathematics means thatit is no longer feasible to provide as many applied units for Further Mathematics, and so there

are fewer Mechanics and Statistics units. However the provision in Decision Mathematicsremains unaltered;

• Mechanics 4 and Statistics 4 are new units, drawing material from a number of units in the previous specification;

• in addition there are some changes to Statistics 1, 2 and 3; these reflect their new status withinthe Advanced GCE, particularly the fact that Statistics 3 is no longer the natural ending point for

those Advanced GCE students whose Applied Mathematics is entirely statistics;

• Advanced Subsidiary Further Mathematics may now be obtained on three AS units. One ofthese is a new Pure Mathematics unit Further Concepts for Advanced Mathematics, FP1;

• the content of Further Concepts for Advanced Mathematics, FP1, depends only on the ASsubject criteria and so is inevitably different from that of the unit which it replaces. This change

has had knock-on effects to the content of the two remaining units in Pure Mathematics;

• the number of subject titles available has been reduced in line with the new subject criteria.

In addition, there are some other changes that are not a direct consequence of the new subject criteria.In particular, those responsible for this specification were aware that, following the introduction of

Curriculum 2000, mathematics was making much greater demands on students’ time than othersubjects and so there is a reduction in the amount of coursework required.


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© MEI/OCR 2013 Section C: General Information 9 Oxford, Cambridge and RSA Examinations MEI Structured Mathematics

SECTION C: GENERAL INFORMATION

1 Introduction

1.1 RATIONALE

1.1.1 This Specif ication

This booklet contains the specification for MEI Structured Mathematics for teaching from September

2013. It covers Advanced Subsidiary GCE (AS) and Advanced GCE (A Level) qualifications inMathematics and Further Mathematics and also in Pure Mathematics.

This specification was developed by Mathematics in Education and Industry (MEI) and is assessed by OCR. Support for those delivering the specification comes from both bodies and this is one of its

particular strengths.

This specification is designed to help more students to fulfil their potential by taking and enjoying

mathematics courses that are relevant to their needs post-16. This involves four key elements:

breadth, depth, being up-to-date and providing students with the ability to use their mathematics.

• Most students at this level are taking mathematics as a support subject. Their needs are almostas diverse as their main fields of study, and consequently this specification includes the breadthof several distinct strands of mathematics: Pure Mathematics, Mechanics, Statistics, Decision

Mathematics and Numerical Analysis.• There are, however, those students who will go on to read mathematics at university and

perhaps then become professional mathematicians. These students need the challenge of taking

the subject to some depth and this is provided by the considerable wealth of Further

Mathematics units in this specification, culminating in FP3, M4 and S4.

• Mathematics has been transformed at this level by the impact of modern technology: thecalculator, the spreadsheet and dedicated software. There are many places where thisspecification either requires or strongly encourages the use of such technology. The units DC,

NC and FPT have computer based examinations; an option in FP3 is based on graphical

calculators, and the coursework in C3 and NM is based on the use of suitable devices.

• Many students complete mathematics courses quite well able to do routine examinationquestions but unable to relate what they have learnt to the world around them. This

specification is designed to provide students with the necessary interpretive and modelling skills

to be able to use their mathematics. Modelling and interpretation are stressed in the papers andsome of the coursework and there is a comprehension paper as part of the assessment of C4.

MEI is a curriculum development body and in devising this specification the long term needs ofstudents have been its paramount concern.

This specification meets the requirements of the Common Criteria (QCA, 1999), the GCE Advanced

Subsidiary and Advanced Level Qualification-Specific Criteria (QCA, 1999) and the Subject Criteria

for Mathematics (QCA, 2002).


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10 Section C: General Information © MEI/OCR 2013 MEI Structured Mathematics Oxford, Cambridge and RSA Examinations

1.1.2 MEI and OCR

MEI is a long established, independent curriculum development body, with a membership consisting

almost entirely of working teachers. MEI provide advice and INSET relating to all the curriculum

and teaching aspects of the course. It also provides teaching materials, and the accompanying series

of textbooks is the product of a partnership between MEI and a major publishing house. A particularfeature of this specification is the very substantial website (see Section 7), covering all the various

units. Students can access this at school or college, or when working at home. Not only does thishelp them with their immediate mathematics course; it also develops the skills they will need for

independent learning throughout their lives.

OCR’s involvement is primarily centred on the assessment, awarding and issuing of results.

However, members of the Qualification Team are available to give advice, receive feedback and give

general support.

OCR also provides INSET and materials such as Examiners’ Reports, mark schemes and past papers.

It is thus a feature of this specification that an exceptional level of help is always available to teachersand students, at the end of the telephone or on-line.

1.1.3 Background

The period leading up to the start of this specification has been a difficult one for post-16

mathematics with a substantial drop in the numbers taking the subject. This specification has beendesigned to redress that situation by ensuring that the various units can indeed be taught and learnt

within the time allocated.

Considerable thought has gone into its design, and from a large number of people, many of them

classroom teachers or lecturers. Those responsible are confident that the specification makes full use

of the new opportunities opened up by the changes to the subject criteria: mathematics will be

accessible to many more students but will also provide sufficient challenge for the most able.

MEI Structured Mathematics was first introduced in 1990 and was subsequently refined in 1994 and

2000 to take account of new subject cores and advice from teachers and lecturers. The philosophy

underlying the 1990 specification was described in its introduction, which is reproduced verbatim

later in this section.

This specification represents a new interpretation of the same philosophy. It takes account not only

of the requirements of the 2002 subject criteria but also of the quite different environment in which post-16 mathematics is now embedded.

The major changes from the previous MEI specification (that for first teaching in September 2000)are outlined for the convenience of users on page 8 of this specification. However, it is more

appropriate to see this as a specification in its own right, which, while building on past experience, is

designed for present-day students working in present-day conditions.


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1.1.4 New Opportunit ies

The new subject criteria, published by QCA in December 2002, are intended to make mathematics

more accessible for students and easier for schools and colleges to deliver within existing time

constraints. This specification is designed to take full advantage of the opportunities this opens up.

The content of the subject core is little changed but it is now spread over four units, two at AS and

two at A2, instead of the previous three. This means that the content of each individual PureMathematics unit is reduced so that more time can be given to teaching the topics within it.

A particular feature of this specification is the first Pure Mathematics unit, C1. It is designed to givestudents a firm foundation in the basic skills that they will need for all their other units, thereby

making advanced study of mathematics accessible to many more people.

Another major new opportunity occurs with Further Mathematics. It is now, for the first time,

possible to obtain AS Further Mathematics on three AS units. In this specification, the first Pure

Mathematics unit, FP1, is a genuine AS unit and students who have been successful at Higher TierGCSE should be able to start studying it at the same time as C1 and C2. It will no longer be

necessary for potential Further Mathematics students to mark time while they learn enough of the

single Mathematics to allow them to get started.

It is however still possible for schools and colleges to deliver Further Mathematics in other ways: for

example by doing three extra units over the two years for the AS qualification. That point illustratesanother feature of this specification, its flexibility. It is designed to meet the needs of a wide range of

students, from those who find AS Level a real challenge to others who are blessed with extraordinary

talent in mathematics. The flexibility also covers the needs of schools and colleges with widelydiffering numbers of post-16 mathematics students.

1.1.5 A Route of Progression

MEI Structured Mathematics is designed not just to be a specification for AS or Advanced GCE

Mathematics but to provide a route of progression through the subject starting from GCSE and going

into what is first year work in some university courses. The specification is also, by design, entirely

suitable for those who are already in employment, or are intending to progress directly into it.

1.1.6 Underlying Philosophy: Introduction to the 1990 Syllabus

This section contains the introduction to the first MEI Structured Mathematics specification and is

included as a statement of underlying philosophy. These were the first modular A Levels in any

subject and their development was accompanied by serious consideration of how the needs ofindustry and adult life could best be addressed through a mathematics specification.

‘Our decision to develop this structure, based on 45-hour Components, for the study of Mathematics

beyond GCSE stems from our conviction, as practising teachers, that it will better meet the needs of

our students. We believe its introduction will result in more people taking the subject at both A and

AS, and that the use of a greater variety of assessment techniques will allow content to be taught andlearnt more appropriately with due emphasis given to the processes involved.


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Mathematics is required by a wide range of students, from those intending to read the subject at

university to those needing particular techniques to support other subjects or their chosen careers.

Many syllabuses are compromises between these needs, but the necessity to accommodate the most

able students results in the content being set at a level which is inaccessible to many, perhaps the

majority of, sixth formers. The choice allowed within this scheme means that in planning courses

centres will be able to select those components that are relevant to their students’ needs, confidentthat the work will be at an appropriate level of difficulty.

While there are some areas of Mathematics which we feel to be quite adequately assessed by formalexamination, there are others which will benefit from the use of alternative assessment methods,

making possible, for example, the use of computers in Numerical Analysis and of substantial sets ofdata in Statistics. Other topics, like Modelling and Problem Solving, have until now been largely

untested because by their nature the time they take is longer than can be allowed in an examination.

A guiding principle of this scheme is that each Component is assessed in a manner appropriate to itscontent.

We are concerned that students should learn an approach to Mathematics that will equip them to useit in the adult world and to be able to communicate what they are doing to those around them. We

believe that this cannot be achieved solely by careful selection of syllabus content and have framed

our Coursework requirements to develop skills and attitudes which we believe to be important.

Students will be encouraged to undertake certain Coursework tasks in teams and to give presentations

of their work. To further a cross-curricular view of Mathematics we have made provision for

suitable Coursework from other subjects to be admissible.

We believe that this scheme will do much to improve both the quantity and the quality of

Mathematics being learnt in our schools and colleges.’

1.2 CERTIFICATION TITLE

This specification will be shown on a certificate as one or more of the following:

• OCR Advanced Subsidiary GCE in Mathematics (MEI)

• OCR Advanced Subsidiary GCE in Further Mathematics (MEI)

• OCR Advanced Subsidiary GCE in Pure Mathematics (MEI)

• OCR Advanced GCE in Mathematics (MEI)

• OCR Advanced GCE in Further Mathematics (MEI)

• OCR Advanced GCE in Pure Mathematics (MEI)

Candidates who complete 15 or 18 units respectively will have achieved at least the equivalent of the

standard of Advanced Subsidiary GCE Further Mathematics and Advanced GCE Further

Mathematics in their additional units. The achievements of such candidates will be recognised by

additional awards in Further Mathematics (Additional) with the code numbers 3897 (AS) and 7897

(Advanced GCE).


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1.3 LANGUAGE

This specification, and all associated assessment materials, are available only in English. The

language used in all question papers will be plain, clear, free from bias and appropriate to the

qualification.

1.4 EXCLUSIONS

1.4.1 Exclusions within this Specification

Qualifications in Further Mathematics are not free-standing. Thus:

• candidates for Advanced Subsidiary GCE in Further Mathematics are required either to haveobtained, or to be currently obtaining, either an Advanced Subsidiary GCE in Mathematics or an

Advanced GCE in Mathematics;

• candidates for Advanced GCE in Further Mathematics are required either to have obtained, or to be currently obtaining, an Advanced GCE in Mathematics.

Advanced Subsidiary GCE in Pure Mathematics may not be taken with any other Advanced

Subsidiary GCE qualification within this specification.

Advanced GCE in Pure Mathematics may not be taken with any other Advanced GCE qualification

within this specification.

1.4.2 Exclusions Relating to other Specifications

No Advanced Subsidiary GCE qualification within this specification may be taken at the same time

as any other Advanced Subsidiary GCE having the same title nor with OCR Free Standing

Mathematics Qualification (Advanced): Additional Mathematics.

No Advanced GCE qualification within this specification may be taken with any other Advanced

GCE having the same title.

Candidates may not obtain certification (under any title) from this specification, based on units from

other mathematics specifications, without prior permission from OCR.

Candidates may not enter a unit from this specification and a unit with the same title from othermathematics specifications.

Every specification is assigned to a national classification code indicating the subject area to which it

belongs. Centres should be aware that candidates who enter for more than one GCE qualification

with the same classification code will have only one grade (the highest) counted for the purpose of

School and College Performance Tables.


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The national classification codes for the subjects covered by this specification are as follows:

Mathematics 2210

Pure Mathematics 2230Further Mathematics 2330

1.5 KEY SKILLS

In accordance with the aims of MEI, this scheme has been designed to meet the request of industry

(e.g. the CBI) that students be provided with opportunities to use and develop Key Skills.

The table below indicates which modules are particularly likely to provide opportunities for the

various Key Skills at Level 3.

Module Communication App licati on o f

Number

Information

Technology

Working with

Others

Improving Own

Learning and

Performance

Problem

Solving

C3 4753

C4 4754

DE 4758

DC 4773

NM 4776

NC 4777

FPT 4798

1.6 CODE OF PRACTICE REQUIREMENTS

All qualifications covered by this specification will comply in all aspects with the GCE Code of

Practice for courses starting in September 2004.

1.7 SPIRITUAL, MORAL, ETHICAL, SOCIAL AND CULTURAL ISSUES

Students are required to examine arguments critically and so to distinguish between truth andfalsehood. They are also expected to interpret the results of modelling exercises and there are times

when this inevitably raises moral and cultural issues. Such issues will not be assessed in theexamination questions; nor do they feature, per se, in the assessment criteria for any coursework

tasks.


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1.8 ENVIRONMENTAL EDUCATION, EUROPEAN DIMENSION AND HEALTH AND

SAFETY ISSUES

While the work developed in teaching this specification may use examples, particularly involving

modelling and statistics, that raise environmental issues, these issues do not in themselves form partof the specification.

The work developed in teaching this specification may at times involve examples that raise healthand safety issues. These issues do not in themselves form part of this specification.

OCR has taken account of the 1988 Resolution of the Council of the European Community and theReport Environmental Responsibility: An Agenda for Further and Higher Education, 1993 in

preparing this specification and associated specimen assessment materials.

Teachers should be aware that students may be exposed to risks when doing coursework. Theyshould apply usual laboratory precautions when experimental work is involved. Students should not

be expected to collect data on their own when outside their Centre.

Teachers should be aware of the dangers of repetitive strain injury for any student who spends a long

time working on a computer.

1.9 AVOIDANCE OF BIAS

MEI and OCR have taken great care in the preparation of this specification and assessment materialsto avoid bias of any kind.

1.10 CALCULATORS AND COMPUTERS

Students are expected to make appropriate use of graphical calculators and computers. The JCQ

document Instructions for conducting examinations, published annually, contains the regulations

regarding the use of calculators in examinations.


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2 Specif ication Aims

2.1 AIMS OF MEI

‘To promote the links between education and industry at Secondary School level, and to producerelevant examination and teaching specifications and support material.’

2.2 AIMS OF THIS SPECIFICATION

This course should encourage students to:

• develop their understanding of mathematics and mathematical processes in a way that promotesconfidence and fosters enjoyment;

• develop abilities to reason logically and recognise incorrect reasoning, to generalise and toconstruct mathematical proofs;

• extend their range of mathematical skills and techniques and use them in more difficult,unstructured problems;

• develop an understanding of coherence and progression in mathematics and of how differentareas of mathematics can be connected;

• recognise how a situation may be represented mathematically and understand the relationship between ‘real world’ problems and standard and other mathematical models and how these can

be refined and improved;

• use mathematics as an effective means of communication;

• read and comprehend mathematical arguments and articles concerning applications of

mathematics;• acquire the skills needed to use technology such as calculators and computers effectively,

recognise when such use may be inappropriate and be aware of limitations;

• develop an awareness of the relevance of mathematics to other fields of study, to the world ofwork and to society in general;

• take increasing responsibility for their own learning and the evaluation of their ownmathematical development.


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3 Assessment Objectives

3.1 APPLICATION TO AS AND A2

This specification requires students to demonstrate the following assessment objectives in the contextof the knowledge, understanding and skills prescribed. The assessment objectives for Advanced

Subsidiary GCE and for Advanced GCE are the same.

Students should be able to demonstrate that they can:

AO1

• recall, select and use their knowledge of mathematical facts, concepts and techniques in avariety of contexts.

AO2

• construct rigorous mathematical arguments and proofs through use of precise statements, logicaldeduction and inference and by the manipulation of mathematical expressions, including the

construction of extended arguments for handling substantial problems presented in unstructured

form.

AO3

• recall, select and use their knowledge of standard mathematical models to represent situations inthe real world;

• recognise and understand given representations involving standard models;

• present and interpret results from such models in terms of the original situation, includingdiscussion of assumptions made and refinement of such models.

AO4

• comprehend translations of common realistic contexts into mathematics;

• use the results of calculations to make predictions, or comment on the context;

• where appropriate, read critically and comprehend longer mathematical arguments or examplesof applications.

AO5

• use contemporary calculator technology and other permitted resources (such as formulae booklets or statistical tables) accurately and efficiently;

• understand when not to use such technology, and its limitations;

• give answers to appropriate accuracy.


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3.2 SPECIFICATION GRID

The table below gives the permitted allocation of marks to assessment objectives for the variousunits. The figures given are percentages. These allocations ensure that any allowable combination of

units for AS Mathematics or Advanced GCE Mathematics satisfies the weightings given in Subject

Criteria for Mathematics.

EntryCode

UnitCode

Unit Name LevelWeighting of Assessment Objective (%)

AO1 AO2 AO3 AO4 AO5

4751 C1 Introduction to Advanced Mathematics AS 40-50 40-50 0-10 0-10 0-5

4752 C2 Concepts for Advanced Mathematics AS 30-40 30-40 5-15 5-15 10-20

4753 C3 Methods for Advanced Mathematics A2 40-45 40-45 0-10 0-10 10-20

4754 C4 Applications of Advanced Mathematics A2 30-35 30-35 10-20 15-25 5-15

4755 FP1 Further Concepts for AdvancedMathematics

AS 35-45 35-45 0-10 0-10 0-10

4756 FP2Further Methods for Advanced

MathematicsA2 35-45 35-45 0-10 0-10 0-10

4757 FP3Further Applications of Advanced

MathematicsA2 35-45 35-45 0-10 0-10 0-10

4758 DE Differential Equations A2 20-30 20-30 25-35 10-20 5-15

4761 M1 Mechanics 1 AS 20-30 20-30 25-35 10-20 5-15

4762 M2 Mechanics 2 A2 20-30 20-30 25-35 10-20 5-15

4763 M3 Mechanics 3 A2 20-30 20-30 25-35 10-20 5-15

4764 M4 Mechanics 4 A2 20-30 20-30 25-35 10-20 5-15

4766 S1 Statistics 1 AS 20-30 20-30 25-35 10-20 5-15

4767 S2 Statistics 2 A2 20-30 20-30 25-35 10-20 5-15

4768 S3 Statistics 3 A2 20-30 20-30 25-35 10-20 5-15

4769 S4 Statistics 4 A2 20-30 20-30 25-35 10-20 5-15

4771 D1 Decision Mathematics 1 AS 20-30 20-30 25-35 10-20 5-15

4772 D2 Decision Mathematics 2 A2 20-30 20-30 25-35 10-20 5-15

4773 DC Decision Mathematics Computation A2 20-30 20-30 25-35 5-15 10-30

4776 NM Numerical Methods AS 30-40 30-40 0-10 0-10 20-30

4777 NC Numerical Computation A2 25-35 25-35 0-10 10-20 20-30

4798 FPTFurther Pure Mathematics with

TechnologyA2 30-40 30-40 0 0 25-40


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4 Scheme of Assessment

4.1 UNITS OF ASSESSMENT

4.1.1 Summary Table

EntryCode

UnitCode

Level Unit NameExamination Questions*

(approximate markallocation)

Time(hours)

4751 C1 AS Introduction to Advanced Mathematics A: 8-10 × ≤ 5 = 36; B: 3 × 12 = 36 1½

4752 C2 AS Concepts for Advanced Mathematics A: 8-10 × ≤ 5 = 36; B: 3 × 12 = 36 1½

4753 C3 A2 Methods for Advanced MathematicsA: 5-7 × ≤ 8 = 36; B: 2 × 18 = 36Coursework: 18

1½

4754 C4 A2

Applications of Advanced Mathematics

Paper A A: 5-7×

≤

8 = 36; B: 2×

18 = 36 1½

Applications of Advanced MathematicsPaper B

Comprehension: 18 1

4755 FP1 ASFurther Concepts for AdvancedMathematics

A: 5-7 × ≤ 8 = 36; B: 3 × 12 = 36 1½

4756 FP2 A2Further Methods for AdvancedMathematics

A: 3 × 18 = 54;B: 1 × 18 = 18

1½

4757 FP3 A2Further Applications of AdvancedMathematics

3 (from 5) × 24 = 72 1½

4758 DE A2 Differential Equations3 (from 4) × 24 = 72;

Coursework: 18

1½

4761 M1 AS Mechanics 1 A: 5-7 × ≤ 8 = 36; B: 2 × 18 = 36 1½

4762 M2 A2 Mechanics 2 4 × 18 = 72 1½

4763 M3 A2 Mechanics 3 4 × 18 = 72 1½

4764 M4 A2 Mechanics 4 A: 2 × 12 = 24; B: 2 × 24 = 48 1½

4766 S1 AS Statistics 1 A: 5-7 × ≤ 8 = 36; B: 2 × 18 = 36 1½

4767 S2 A2 Statistics 2 4 × 18 = 72 1½

4768 S3 A2 Statistics 3 4 × 18 = 72 1½

4769 S4 A2 Statistics 4 3 (from 4) × 24 = 72 1½

4771 D1 AS Decision Mathematics 1 A: 3 × 8 = 24; B: 3 × 16 = 48 1½4772 D2 A2 Decision Mathematics 2 A: 2 × 16 = 32; B: 2 × 20 = 40 1½

4773 DC A2 Decision Mathematics Computation 4 × 18 = 72 2½

4776 NM AS Numerical MethodsA: 5-7 × ≤ 8 = 36; B: 2 × 18 = 36Coursework: 18

1½

4777 NC A2 Numerical Computation 3 (from 4) × 24 = 72 2½

4798 FPT A2Further Pure Mathematics withTechnology

3 × 24 = 72 2

* number of questions x number of marks for each = total mark

For Units 4753, 4758 and 4776, Centres have the option of submitting new coursework (entry code Option

A) or carrying forward a coursework mark from a previous session (Option B).


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4.1.2 Weighting

For all certifications, the contribution of each unit is the same. Thus each unit carries 331/3% of the

total marks for an Advanced Subsidiary certification and 162/3% of the total marks for an Advanced

GCE certification.

4.2 STRUCTURE

4.2.1 Recommended Order

The assumed knowledge required to start any unit is stated on the title page of its specification. In

general, students are recommended to take the units in any strand in numerical order.

Students will also find it helpful to refer to the diagram on the cover of this specification and also on

page 5. The lines connecting the various units indicate the recommended order and the positions (left

to right) of the units indicate their level of sophistication.

The assessment of a unit may require work from an earlier unit in the same strand. However such

earlier work will not form the focus of a question. This specification has been designed so that in

general the applied modules are supported by the techniques in the pure modules at the same level.

Where this is not the case, it is highlighted on the unit’s title page.

There are, however, no formal restrictions on the order in which units may be taken.

4.2.2 Constraints

A student’s choice of units for these awards is subject to the following restrictions (a) to (d).

(a) Mathematics and Further Mathematics Subject Criteria: Compulsory Units

Combinations of units leading to certifications entitled Mathematics and Further Mathematics arerequired to cover the mathematics subject criteria. The content of this is covered by the following

compulsory units.

Mathematics

Advanced Subsidiary GCE: C1, Introduction to Advanced MathematicsC2, Concepts for Advanced Mathematics

Advanced GCE: C1, Introduction to Advanced MathematicsC2, Concepts for Advanced Mathematics

C3, Methods for Advanced Mathematics

C4, Applications of Advanced Mathematics


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Further Mathematics

Advanced Subsidiary GCE: FP1, Further Concepts for Advanced Mathematics

Advanced GCE: FP1, Further Concepts for Advanced MathematicsFP2, Further Methods for Advanced Mathematics

(b) Balance between Pure and Applied Units

There must be a balance between pure and applied mathematics. There must be one applied unit in

AS Mathematics and two applied units in Advanced GCE Mathematics.

Pure Units Applied Units

C1, Introduction to Advanced Mathematics

C2, Concepts for Advanced Mathematics



FP1, Further Concepts for Advanced Mathematics

FP2, Further Methods for Advanced Mathematics

FP3, Further Applications of Advanced

Mathematics

NM, Numerical Methods

NC, Numerical Computation

FPT, Further Pure Mathematics with Technology

DE, Differential Equations

M1, Mechanics 1

M2, Mechanics 2

M3, Mechanics 3

M4, Mechanics 4

S1, Statistics 1

S2, Statistics 2

S3, Statistics 3

S4, Statistics 4

D1, Decision Mathematics 1

D2, Decision Mathematics 2

DC, Decision Mathematics Computation

(c) AS and A2 Units

AS GCE Mathematics consists of three AS units.

Advanced GCE Mathematics consists ofeither three AS units and three A2 units

or four AS units and two A2 units.


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(d) Mathematics Units not allowed in Further Mathematics

The following units cover the Subject Criteria for Advanced GCE Mathematics and so may not

contribute to Further Mathematics awards.

C1, Introduction to Advanced Mathematics

C2, Concepts for Advanced Mathematics



These units may, however, contribute towards awards in Pure Mathematics, but only as described in

Sections 4.3.7 and 4.3.8.

4.2.3 Synoptic Assessment

The subject criteria for mathematics require that any combination of units valid for the certification

of Advanced GCE Mathematics (7895) or Advanced GCE Pure Mathematics (7898) must include a

minimum of 20% synoptic assessment.

Synoptic assessment in mathematics addresses candidates’ understanding of the connections between

different elements of the subject. It involves the explicit drawing together of knowledge,

understanding and skills learned in different parts of the Advanced GCE course through using and

applying methods developed at earlier stages of study in solving problems. Making and

understanding connections in this way is intrinsic to mathematics.

In this specification the Units C1 to C4 contribute over 30% synoptic assessment and so all valid

combinations of units meet the synoptic requirement. There is also a further contribution from thetwo applied units in Advanced GCE Mathematics and from the two further pure units in Advanced

GCE Pure Mathematics.

There are no requirements concerning synoptic assessment relating to the certification of Advanced

Subsidiary GCE or to Advanced GCE Further Mathematics.

4.3 RULES OF COMBINATION

4.3.1 Advanced Subsidiary GCE Mathematics (3895)

Candidates take one of the following combinations of units:

either C1, C2 and M1

or C1, C2 and S1 or C1, C2 and D1

No other combination of units may be used to claim AS GCE Mathematics.


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4.3.2 Advanced GCE Mathematics (7895)

All Advanced GCE Mathematics combinations include:

C1, C2, C3 and C4.

The other two units must be one of the following combinations:

M1, M2; S1, S2; D1, D2; D1, DC; M1, S1; M1, D1; S1, D1

No other combination of units may be used to claim Advanced GCE Mathematics.

The entry codes for these units are repeated here for the convenience of users.

C1 4751 M1 4761 S1 4766 D1 4771

C2 4752 M2 4762 S2 4767 D2 4772

C3 4753 DC 4773

C4 4754

4.3.3 Advanced Subsidiary GCE Further Mathematics (3896)

Candidates for Advanced Subsidiary GCE Further Mathematics will be expected to have obtained, orto be obtaining concurrently, either Advanced Subsidiary or Advanced GCE Mathematics.

The three units for Advanced Subsidiary GCE Further Mathematics must include:

FP1

The remaining two units may be any two other units subject to the conditions that:

• a total of six different units are required for certification in Advanced Subsidiary GCEMathematics and Advanced Subsidiary GCE Further Mathematics;

• a total of nine different units are required for certification in Advanced GCE Mathematics andAdvanced Subsidiary GCE Further Mathematics.

Candidates who certificate for Advanced Subsidiary GCE Futher Mathematics before certificatingfor Advanced GCE Mathematics are strongly advised to recertificate for all previously entered

qualifications whenever they subsequently make an entry for a qualification.

4.3.4 Advanced GCE Further Mathematics (7896)

Candidates for Advanced GCE Further Mathematics will be expected to have obtained, or to be

obtaining concurrently, Advanced GCE Mathematics.

The six units for Advanced GCE Further Mathematics must include both:

FP1; FP2


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The remaining four units may be any four other units subject to the conditions that:

• a total of 12 different units are required for certification in Advanced GCE Mathematics andAdvanced GCE Further Mathematics;

• at least two of the four units are A2 units.

4.3.5 Additional Qualification in Advanced Subsidiary GCE FurtherMathematics (3897)

Candidates who offer 15 units are eligible for an additional award in Advanced Subsidiary GCEFurther Mathematics. Such candidates must have fulfilled the requirements for Advanced GCE

Mathematics and Advanced GCE Further Mathematics.

4.3.6 Additional Qualifi cation in Advanced GCE Further Mathematics (7897)

Candidates who offer 18 units are eligible for an additional award in Advanced GCE FurtherMathematics. Such candidates must have fulfilled the requirements for Advanced GCE Mathematics

and Advanced GCE Further Mathematics.

4.3.7 Advanced Subsidiary GCE Pure Mathematics (3898)

Candidates take one of the following combinations of units:

eitherC1, C2

andFP1

or C1, C2 and NM

or C1, C2 and C3

or C1, C2 and C4

No other combination of units may be used to claim AS GCE Pure Mathematics.

A qualification in AS Pure Mathematics may not be obtained in the same series in combination with

any qualification in Mathematics or Further Mathematics.

4.3.8 Advanced GCE Pure Mathematics (7898)

All Advanced GCE Pure Mathematics combinations include:

C1, C2, C3 and C4.

The other two units must be one of the following combinations:

FP1, FP2; FP1, FP3; FP1, NC; NM, FP2; NM, FP3; NM, NC

No other combination of units may be used to claim Advanced GCE Pure Mathematics.


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A qualification in Advanced GCE Pure Mathematics may not be obtained in the same series in

combination with any qualification in Mathematics or Further Mathematics.

4.4 FINAL CERTIFICATION

Each unit is given a grade and a Uniform Mark, using procedures laid down by Ofqual in thedocument GCE A and AS Code of Practice. The relationship between total Uniform Mark and

subject grade follows the national scheme.

4.4.1 Certi fication of Mathematics

Candidates enter for three units of assessment at Advanced Subsidiary GCE. To complete the

Advanced GCE candidates must enter a valid combination of six units.

To claim an award at the end of the course, candidates’ unit results must be

aggregated. This does not happen automatically and Centres must make separate‘certification entries’.

Candidates may request certification entries for:

either Advanced Subsidiary GCE aggregation

or Advanced Subsidiary GCE aggregation, bank the result, and complete the A2 assessment

at a later dateor Advanced GCE aggregation

or Advanced Subsidiary GCE and Advanced GCE aggregation in the same series.

Candidates must enter the appropriate AS and A2 units to qualify for the full Advanced GCE award.

4.4.2 Certi fication of Mathematics and Further Mathematics: Order of Aggregation

Units that contribute to an award in Advanced GCE Mathematics may not also be used for an award

in Advanced GCE Further Mathematics. Candidates who are awarded certificates in both Advanced

GCE Mathematics and Advanced GCE Further Mathematics must use unit results from 12 different

teaching modules. Candidates who are awarded certificates in both Advanced GCE Mathematics and

Advanced Subsidiary GCE Further Mathematics must use unit results from nine different teaching

modules. Candidates who are awarded certificates in both Advanced Subsidiary GCE Mathematicsand Advanced Subsidiary GCE Further Mathematics must use unit results from six different teaching

modules.

When a candidate has requested awards in both Mathematics and Further Mathematics, OCR will

adopt the following procedures which follow the GCE Mathematics Aggregation Rules, available onthe JCQ website.

If certification for Advanced GCE Mathematics is made at the same time as the request for a Further

Mathematics certification then the valid combination of units will be chosen that gives, in decreasing

order of priority:

• the best possible grade for Mathematics;


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• the best possible grade for Further Mathematics;

• the highest possible UMS in Mathematics.

Note: In the aggregation process, in order to achieve the best set of grades for a candidate as

described above, it is possible that AS GCE Further Mathematics may include some A2 units.

If the only certifications being requested are Advanced Subsidiary GCE Mathematics at the same

time as Advanced Subsidiary GCE Further Mathematics then the valid combination of units will bechosen that gives, in decreasing order of priority:

• the best possible grade for AS Mathematics;

• the best possible grade for AS Further Mathematics;

• the highest possible UMS in AS Mathematics.

Candidates are strongly advised to recertificate any previously entered qualifications wheneveran entry is made for a qualification. This allows the grades awarded to be optimised according tothe JCQ rules. For example, if a candidate sits A level Mathematics the units used towards that

qualification are ‘locked’ into Mathematics. If the candidate then enters for AS or A level Further

Mathematics in a subsequent series, only the unused units are available for use in Further

Mathematics. Recertification of all previously entered qualifications unlocks all units and allows the

optimisation of the pair of grades awarded.

4.4.3 Awarding of Grades

The Advanced Subsidiary has a weighting of 50% when used in an Advanced GCE award.

Advanced GCE awards are based on the aggregation of the weighted Advanced Subsidiary (50%)and A2 (50%) Uniform Marks

Advanced Subsidiary GCE qualifications are awarded on the scale A to E or U (unclassified).Advanced GCE qualifications are awarded on the scale A* to E or U (unclassified).

4.4.4 Extra Units

A candidate may submit more than the required number of units for a subject award (for example,seven instead of six for an Advanced GCE). In that case the legal combination for that award which

is most favourable to the candidate will be chosen.

4.4.5 Enquir ies on Results

Candidates will receive their final unit results at the same time as their subject results. In common

with other Advanced GCE results, the subject results are at that stage provisional to allow enquiries

on results. Enquiries concerning marking are made at the unit level and so only those units taken at

the last sitting may be the subject of such appeals. Enquiries are subject to OCR’s generalregulations.


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4.5 AVAILABILITY

4.5.1 Unit Availabil ity

From September 2013, there is one examination series each year, in June.In June all units are assessed.

4.5.2 Certi fication Availabil ity

Certification is available in the June series only.

4.5.3 Shelf-life of Units

Individual unit results, prior to certification of the qualification, have a shelf-life limited only by thatof the specifications.

4.6 RE-SITS

4.6.1 Re-si ts of Units

There is no limit to the number of times a candidate may re-sit a unit. The best result will count.

4.6.2 Re-sits of Advanced Subsidiary GCE and Advanced GCE

Candidates may take the whole qualification more than once.


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4.7 QUESTION PAPERS

4.7.1 Style of Question Papers

The assessment requirements of the various units are summarised in the table in Section 4.1.1.

Most units are assessed by a single question paper lasting 1½ hours. The exceptions are as follows:

• there is also a coursework requirement in C3, DE and NM ;

• the examinations for DC and NC last 2½ hours;

• the examination for FPT lasts 2 hours;

• there are two parts to the examination for C4. As well as the 1½ hour Paper A (with twosections) there is a comprehension paper lasting 1 hour (Paper B).

Many of the question papers have two sections, A and B. The questions in Section A are short andtest techniques. The questions in Section B are longer and also test candidates’ ability to follow a

more extended piece of mathematics.

In most papers there is no choice of questions but there are options in the papers for the following

units: FP3, DE, S4 and NC .

4.7.2 Use of Language

Candidates are expected to use clear, precise and appropriate mathematical language, as described inAssessment Objective 2.

4.7.3 Standard

Candidates and Centres must note that each A2 unit is assessed at Advanced GCE standard and that

no concessions are made to any candidate on the grounds that the examination has been taken early

in the course. Centres may disadvantage their candidates by entering them for a unit examination

before they are ready.

4.7.4 Thresholds

At the time of setting, each examination paper will be designed so that 50% of the marks areavailable to grade E candidates , 75% to grade C and 100% to grade A. Typically candidates are

expected to achieve about four fifths of the marks available to achieve a grade, giving design gradesof : A 80%, B 70%, C 60%, D 50% and E 40%. The actual grading is carried out by the Awarding

Committee. They make allowance for examination performance and for any features of a particular

paper that only become apparent after it has been taken. Thus some variation from the design grades

can be expected in the award.


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4.7.5 Calculators

No calculating aids may be used in the examination for Unit C1. For all other units, a graphical

calculator is allowed. Computers, and calculators with computer algebra functions, are not permitted

in answering any of the units with the exceptions of DC, NC and FPT . The JCQ document Instructions for conducting examinations, published annually, contains the regulations regarding the

use of calculators in examinations.

4.7.6 Mathematical Formulae and Statistical Tables

A booklet (MF2, January 2007 version) containing Mathematical Formulae and Statistical Tables is

available for the use of candidates in all unit examinations.

Details of formulae which candidates are expected to know and the mathematical notation that will be used in question papers are contained in Appendices A and B.

A fuller booklet, entitled Students’ Handbook , is also available for students’ use during the course.

This includes all relevant formulae for each unit; those that students are expected to know are

identified. The Students’ Handbook also includes a list of the notation to be used and the statistical

tables. Schools and colleges needing copies for their students’ use may obtain them from the MEI

Office (see Section 7 for the address).

4.8 COURSEWORK

4.8.1 Rationale

The requirements of the following units include a single piece of coursework, which will count for

20% of the assessment of the unit:


DE, Differential Equations

NM, Numerical Methods.

In each case the coursework covers particular skills or topics that are, by their nature, unsuitable forassessment within a timed examination but are nonetheless important aspects of their modules.

The work undertaken in coursework is thus of a different kind from that experienced in examinations.

As a result of the coursework, students should gain better understanding of how mathematics isapplied in real-life situations.

4.8.2 Use of Language

Candidates are expected to use clear, precise and appropriate mathematical language, as described in

Assessment Objective 2.


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4.8.3 Guidance

Teachers should give students such guidance and instruction as is necessary to ensure that they

understand the task they have been given, and know how to set about it. They should explain the

basis on which it will be assessed. Teachers should feel free to answer reasonable questions and to

discuss students’ work with them, until the point where they are working on their final write-up.

A student who takes up and develops advice offered by the teacher should not be penalised for doing

so. Teachers should not leave students to muddle along without any understanding of what they are

doing. If, however, a student needs to be led all the way through the work, this should be taken into

account in the marking, and a note of explanation written on the assessment sheet. Teachers shouldappreciate that a moderator can usually detect when a student has been given substantial help and that

it is to the student’s disadvantage if no mention is made of this on the assessment sheet.

Students may discuss a task freely among themselves and may work in small groups. The finalwrite-up must, however, be a student’s own work. It is not expected that students will work in larger

groups than are necessary.

Coursework may be based on work for another subject (e.g. Geography or Economics), where this is

appropriate, but the final write-up must be submitted in a form appropriate for Mathematics.

In order to obtain marks for the assessment domain Oral Communication, students must either give a

presentation to the rest of the class, have an interview with the assessor or be engaged in on-going

discussion.

4.8.4 Coursework Tasks

Centres are free to develop their own coursework tasks and in that case they may seek advice from

OCR about the suitability of a proposed task in relation both to its subject content and its assessment.

However, Centres that are new to the scheme are strongly advised to start with tasks in the MEIfolder entitled Coursework Resource Material. This is available from the MEI Office (see Section 7

for address).

4.8.5 Moderation

Coursework is assessed by the teacher responsible for the module or by someone else approved by

the Centre. It should be completed and submitted within a time interval appropriate to the task.

Consequently the teacher has two roles. While the student is working on coursework, the teacher

may give assistance as described earlier. However, once the student has handed in the final write-up,the teacher becomes the assessor and no further help may be given. Only one assessment of a piece

of coursework is permitted; it may not be handed back for improvement or alteration.

The coursework is assessed over a number of domains according to the criteria laid down in the unit

specification. The method of assessment of Oral Communication should be stated and a brief reporton the outcome written in the space provided on the assessment sheet.


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4.8.6 Internal Standardisation

Centres that have more than one teaching group for a particular module must carry out internal

standardisation of the coursework produced to ensure that a consistent standard is being maintained

across the different groups. This must be carried out in accordance with guidelines from OCR. An

important outcome of the internal standardisation process will be the production of a rank order of allcandidates.

4.8.7 External Moderation

After coursework is marked by the teacher and internally standardised by the Centre, the marks are

then submitted to OCR by the specified date, after which postal moderation takes place in accordancewith OCR procedures. Centres must ensure that the work of all the candidates is available for

moderation.

As a result of external moderation, the coursework marks of a Centre may be changed, in order toensure consistent standards between Centres.

4.8.8 Re-Sits

If a unit is re-taken, candidates are offered the option of submitting new coursework (Entry Code

Option A) or carrying over the coursework mark from a previous session (Option B).

4.8.9 Minimum Coursework Requirements

If a candidate submits no work for the coursework component, then the candidate should be indicated

as being absent from that component on the coursework Mark Sheet submitted to OCR. If a

candidate completes any work at all for the coursework component then the work should be assessed

according to the criteria and marking instructions and the appropriate mark awarded, which may be

0 (zero).

4.8.10 Authentication

As with all coursework, Centres must be able to verify that the work submitted for assessment is the

candidate’s own work.

4.9 SPECIAL ARRANGEMENTS

For candidates who are unable to complete the full assessment or whose performance may be unduly

affected through no fault of their own, teachers should consult the JCQ booklet Access Arrangements, Reasonable Adjustments and Special Consideration. In such cases advice should be

sought from OCR as early as possible during the course.


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4.10 DIFFERENTIATION

In the question papers differentiation is achieved by setting questions which are designed to assess

candidates at their appropriate levels of ability and which are intended to allow candidates to

demonstrate what they know, understand and can do.

In coursework, differentiation is by task and by outcome. Students undertake assignments which

enable them to display positive achievement.

4.11 GRADE DESCRIPTIONS

The following grade descriptions indicate the level of attainment characteristic of the given grade at

Advanced GCE. They give a general indication of the required learning outcomes at each specified

grade. The descriptions should be interpreted in relation to the content outlined in the specification;

they are not designed to define that content. The grade awarded will depend in practice upon the

extent to which the candidate has met the assessment objectives overall. Shortcomings in some

aspects of the examination may be balanced by better performances in others.

Grade A

Candidates recall or recognise almost all the mathematical facts, concepts and techniques that are

needed, and select appropriate ones to use in a wide variety of contexts.

Candidates manipulate mathematical expressions and use graphs, sketches and diagrams, all with

high accuracy and skill. They use mathematical language correctly and proceed logically and

rigorously through extended arguments or proofs. When confronted with unstructured problems they

can often devise and implement an effective solution strategy. If errors are made in their calculationsor logic, these are sometimes noticed and corrected.

Candidates recall or recognise almost all the standard models that are needed, and select appropriate

ones to represent a wide variety of situations in the real world. They correctly refer results fromcalculations using the model to the original situation; they give sensible interpretations of their results

in the context of the original realistic situation. They make intelligent comments on the modelling

assumptions and possible refinements to the model.

Candidates comprehend or understand the meaning of almost all translations into mathematics of

common realistic contexts. They correctly refer the results of calculations back to the given context

and usually make sensible comments or predictions. They can distil the essential mathematical

information from extended pieces of prose having mathematical content. They can comment

meaningfully on the mathematical information.

Candidates make appropriate and efficient use of contemporary calculator technology and other

permitted resources, and are aware of any limitations to their use. They present results to anappropriate degree of accuracy.


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Grade C

Candidates recall or recognise most of the mathematical facts, concepts and techniques that are

needed, and usually select appropriate ones to use in a variety of contexts.

Candidates manipulate mathematical expressions and use graphs, sketches and diagrams, all with areasonable level of accuracy and skill. They use mathematical language with some skill and

sometimes proceed logically through extended arguments or proofs. When confronted withunstructured problems they sometimes devise and implement an effective and efficient solution

strategy. They occasionally notice and correct errors in their calculations.

Candidates recall or recognise most of the standard models that are needed and usually select

appropriate ones to represent a variety of situations in the real world. They often correctly refer

results from calculations using the model to the original situation; they sometimes give sensibleinterpretations of their results in the context of the original realistic situation. They sometimes make

intelligent comments on the modelling assumptions and possible refinements to the model.

Candidates comprehend or understand the meaning of most translations into mathematics of common

realistic contexts. They often correctly refer the results of calculations back to the given context and

sometimes make sensible comments or predictions. They distil much of the essential mathematical

information from extended pieces of prose having mathematical content. They give some useful

comments on this mathematical information.

Candidates usually make appropriate and efficient use of contemporary calculator technology andother permitted resources, and are sometimes aware of any limitations to their use. They usually

present results to an appropriate degree of accuracy.

Grade E

Candidates recall or recognise some of the mathematical facts, concepts and techniques that are

needed, and sometimes select appropriate ones to use in some contexts.

Candidates manipulate mathematical expressions and use graphs, sketches and diagrams, all with

some accuracy and skill. They sometimes use mathematical language correctly and occasionally

proceed logically through extended arguments or proofs.

Candidates recall or recognise some of the standard models that are needed and sometimes selectappropriate ones to represent a variety of situations in the real world. They sometimes correctly refer

results from calculations using the model to the original situation; they try to interpret their results inthe context of the original realistic situation.

Candidates sometimes comprehend or understand the meaning of translations in mathematics ofcommon realistic contexts. They sometimes correctly refer the results of calculations back to the

given context and attempt to give comments or predictions. They distil some of the essential

mathematical information from extended pieces of prose having mathematical content. They attemptto comment on this mathematical information.

Candidates often make appropriate and efficient use of contemporary calculator technology and other

permitted resources. They often present results to an appropriate degree of accuracy.


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5 Subject Content

5.1 ASSUMED KNOWLEDGE

There is no formal prerequisite for a student wishing to embark on MEI Structured Mathematics.

The unit specifications are written with the same assumption about prior knowledge as that used for

the subject criteria, that students embarking on AS and Advanced GCE study in Mathematics areexpected to have achieved at least grade C in GCSE Mathematics, or its equivalent, and to have

covered all the material in the Intermediate Tier*. Consequently everything which is in the National

Curriculum up to and including that level is also implicit in this specification. In a number of cases

such material is included in the specification for clarity and completeness and is indicated by an

asterisk; such material will not form the focus of an examination question.

*This refers to the Intermediate tier of GCSE Mathematics at the time when the subject criteria werewritten. See the document Assumed Knowledge for GCE Mathematics on the Mathematics pages of

the OCR website (www.ocr.org.uk ) for more details.

http://www.ocr.org.uk/http://www.ocr.org.uk/http://www.ocr.org.uk/http://www.ocr.org.uk/


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5.2 MODELLING

The process of modelling is illustrated by the flow chart below.

1 A problem

2

Make assumptions toallow work to begin

3M

Represent theproblem in

mathematical form

8

Review assumptions

3E

Design anexperiment

4M

Solve themathematical

problem to producetheoretical results

TheModelling

Cycle

TheExperimental

Cycle

4E

Conduct anexperiment andderive practical

results

No5MSelect informationfrom experience,

experiment orobservation

5E

Give a theoreticalinterpretation of

results

7

Is thesolution

of the problemsatisfactory?

6M

Compare withtheoretical results

6E

Compare withexperimental

results

Yes

9

Present findings


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5.3 COMPETENCE STATEMENTS

The unit specifications include competence statements. These are designed to help users byclarifying the requirements, but the following three points need to be noted:

• work that is covered by a competence statement may be asked in an examination questionwithout further assistance being given;

• examination questions may require candidates to use two or more competence statements at thesame time without further assistance being given;

• where an examination question requires work that is not covered by a competence statement,sufficient guidance will be given within the question.

Competence statements have an implied prefix of the words: ‘A student should …’

The letters used in assigning reference numbers to competence statements are as follows.

a algebra A Algorithms b bivariate data B

c calculus C Curves, Curve sketching

d dynamics D Data presentation

e equations E

f functions F

g geometry, graphs G Centre of mass

h Hooke’s law H Hypothesis testing

i impulse and momentum I Inference

j complex numbers Jk kinematics K

l L Linear programming

m matrices M Matchings

n Newton’s laws N Networks

o oscillations (SHM) O

p mathematical processes(modelling, proof, etc)

P Polar coordinates

q dimensions (quantities) Q

r rotation R Random variabless sequences and series S

t trigonometry T Number Theory

u probability (uncertainty) U Errors (uncertainty)

v vectors V

w work, energy and power W

x experimental design X Critical path analysis

y projectiles Y

z Z Simulation


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6 Unit Specif ications

6.1 INTRODUCTION TO ADVANCED MATHEMATICS, C1 (4751) AS

Objectives

To build on and develop the techniques students have learnt at GCSE so that they acquire the fluency

required for advanced work.

Assessment

Examination (72 marks)

1 hour 30 minutes.The examination paper has two sections.

Section A: 8-10 questions, each worth no more than 5 marks.Section Total: 36 marks

Section B: three questions, each worth about 12 marks.Section Total: 36 marks

Assumed Know ledge

Candidates are expected to know the content of Intermediate Tier GCSE*.

*See note on page 34.

Subject Criteria

The Units C1 and C2 are required for Advanced Subsidiary GCE Mathematics in order to ensurecoverage of the subject criteria.

The Units C1, C2, C3 and C4 are required for Advanced GCE Mathematics in order to ensure

coverage of the subject criteria.

Calculators

No calculator is allowed in the examination for this module.

In the MEI Structured Mathematics specification, graphical calculators are allowed in theexaminations for all units except C1.


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INTRODUCTION TO ADVANCED MATHEMATICS, C1

Specifi cation Ref. Competence Statements

Competence statements marked with an asterisk * are assumed knowledge and will not form the

basis of any examination questions. These statements are included for clarity and completeness.

MATHEMATICAL PROCESSES

Proof

The construction and presentation of mathematical arguments through appropriate use of logical

deduction and precise statements involving correct use of symbols and appropriate connecting

language pervade the whole of mathematics at this level. These skills, and the Competence

Statements below, are requirements of all the modules in these specifications.

Mathematicalargument

C1p1 Understand and be able to use mathematical language, grammar andnotation with precision.

2 Be able to construct and present a mathematical argument.

Modelling

Modelling pervades much of mathematics at this level and a basic understanding of the processes

involved will be assumed in all modules

The Modelling Cycle

The modellingcycle.

C1p3 Be able to recognise the essential elements in a modelling cycle.


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Ref. Notes Notation Exclusions

C1p1 Equals, does not equal, identically equals, therefore, because,implies, is implied by, necessary, sufficient

=, ≠, ∴,⇒, ⇐, ⇔

2 Construction and presentation of mathematical argumentsthrough appropriate use of logical deduction and precisestatements involving correct use of symbols and appropriateconnecting language.

3 The elements are illustrated on the diagram in Section 5.2.


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Specification Ref. Competence Statements

ALGEBRA

The basic languageof algebra.

C1a1 Know and be able to use vocabulary and notation appropriate to the subject at thislevel.

Solution ofequations.

2 * Be able to solve linear equations in one unknown.

3 Be able to change the subject of a formula.

4 Know how to solve an equation graphically.

5 Be able to solve quadratic equations.

6 Be able to find the discriminant of a quadratic function and understand itssignificance.

7 Know how to use the method of completing the square to find the line ofsymmetry and turning point of the graph of a quadratic function.

8 * Be able to solve linear simultaneous equations in two unknowns.

9 Be able to solve simultaneous equations in two unknowns where one equation islinear and one is of 2nd order.

10 Know the significance of points of intersection of two graphs with relation to thesolution of simultaneous equations.

Inequalities. 11 Be able to solve linear inequalities.12 Be able to solve quadratic inequalities.

Surds. 13 Be able to use and manipulate surds.

14 Be able to rationalise the denominator of a surd.

Indices. 15 Understand and be able to use the laws of indices for all rational exponents.

16 Understand the meaning of negative, fractional and zero indices.


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Ref. Notes Notation Exclusions

ALGEBRA

C1a1 Expression, function, constant, variable, term, coefficient,index, linear, identity, equation.

f ( ) x Formal treatment offunctions.

2 Including those containing brackets and fractions.

3 Including cases where the new subject appears on both sidesof the original formula, and cases involving squares andsquare roots.

4 Including repeated roots.

5 By factorising, completing the square, using the formula andgraphically.

6 The condition for distinct real roots is: Discriminant > 0The condition for repeated roots is: Discriminant = 0

Discriminant2 4b ac= − .

Complex roots.

7 The graph of 2( ) y a x p q= + + has a turning point at:( , ) p q− and a line of symmetry x p= −

8 By elimination, substitution and graphically.

9 Analytical solution by substitution.

10

11 Including those containing brackets and fractions.12 Algebraic and graphical treatment of quadratic inequalities. Examples involving

quadratics which cannot be factorised.

13

14e.g.

1 5 3

225 3

−=

+

15 , , ( )a b a b a b a b a n an x x x x x x x x+ −× = ÷ = =

16 11

,a

aa x x x

−

= = a

x ,0

1 x =


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Specification Ref. Competence Statements

COORDINATE GEOMETRY

The coordinategeometry ofstraight lines.

C1g1 *Know the equation y mx c= + .

2 Know how to specify a point in Cartesian coordinates in two dimensions.

3 Know the relationship between the gradients of parallel lines and perpendicularlines.

4 * Be able to calculate the distance between two points.

5 * Be able to find the coordinates of the midpoint of a line segment joining two points.

6 Be able to form the equation of a straight line.

7 Be able to draw a line when given its equation.

8 Be able to find the point of intersection of two lines.

The coordinategeometry ofcurves.

9 * Know how to plot a curve given its equation.

10 Know how to find the point of intersection of a line and a curve.

11 Know how the find the point(s) of intersection of two curves.

12 Understand that the equation of a circle, centre (0, 0), radius r is 2 2 2 x y r + =

13 Understand that 2 2 2( ) ( ) x a y b r − + − = is the equation of a circle with centre( , )a b and radius r .

14 Know that: – the angle in a semicircle is a right angle; – the perpendicular from the centre of a circle to a

Documents

75811 Specification